Revolutionizing Bolt Strength Testing 🔩 A Fast Analytical Method for Threaded Connections

The Main Idea

This research presents a fast and accurate analytical method for modeling the elastic–plastic behavior of threaded screw–nut–washer connections, offering a reliable alternative to time-consuming finite element simulations.

The R&D

Threaded connections (you know—bolts and nuts 🔩🔧) are everywhere in engineering: bridges, engines, buildings, wind turbines, and even space rockets! These seemingly simple parts play a crucial role in keeping large structures safe and intact. But here’s the twist: understanding how they behave under real-life stress (not just in ideal scenarios) is still a complex challenge for engineers. Especially when these connections go beyond their elastic limits into the plastic zone—where things start to deform permanently.

Traditionally, engineers relied on super-detailed simulations like Finite Element Analysis (FEA) to study this. While accurate, FEA can be slow and too specific. You can't run 1000 design variations overnight with it. But a new research paper by Carlo Brutti, Corrado Groth, and Marco Evangelos Biancolini from the University of Rome Tor Vergata might just change that! 🏗️

They’ve developed a fast analytical method that accurately models both the elastic and plastic behavior of screw–nut–washer (SNW) assemblies—without needing FEA every time. Let’s break it down in easy terms. 💡

🧠 The Problem with Threads (Not the Social Media Kind)

Threaded joints are complicated because:

• The load distribution isn't even. The first few threads usually take on the most stress. 😰
• Under real loads, parts of the bolt or nut may start to yield (go plastic) before you expect it.
• Most existing methods assume everything stays elastic—not realistic!
• Detailed FEA models take a lot of time and computer power 💻⚙️

So, engineers either get slow but accurate (FEA), or fast but simplistic (classic equations). Until now.

🛠️ The Classic Method, Reimagined

The new method builds on an old idea from the 1930s called Maduschka’s method, which modeled a bolt as a stack of rings (collars) where each thread engagement shares part of the load. Maduschka’s method was simple and good—for elastic materials.

🧪 This paper extends that idea into the plastic zone using smart mathematical enhancements and updated stress-strain models.

Key innovations

• Elastic–perfectly plastic modeling: Tracks how plastic strain grows from the first yield point to full plasticization.
• Improved thread compliance: Uses a modified version of Rankin's Bessel-based solution to more accurately capture how threads deform.
• Handles real-world geometries: Supports ISO thread sizes M16 to M36, and more.
• Matches 2D and 3D FEA results within 5% accuracy—but way faster!

🧮 A Peek Inside the Math

This part gets technical, but here’s the digest:

1. The authors define stress and strain equations for both the screw and the nut, including axial and radial effects.
2. They introduce an iterative, step-by-step method to simulate how threads behave as they start to yield.
3. The method works through load steps, recalculating compliance at each stage—so it keeps up with how the material behavior changes.
4. Critical yield points are defined:
   • 🟡 Yield Start (YS): Where stress first exceeds the yield limit.
   • 🔴 Yield End (YE): Where the whole thread is plastic.

The researchers use von Mises stress as their guide to identify plastic zones. The thread basically “gives up” and transfers more load to the next one.

⚙️ Validated Against Finite Element Simulations

To prove their method works, the team built both 2D axisymmetric and full 3D finite element models of threaded joints in different sizes (M16 to M36). 🧩

They checked:

• Load distribution among threads
• Stress at the critical points
• Yield start and end loads
• Total load capacity

🎯 Result: Their fast method matched FEA results within ~5%, which is excellent for engineering work!

They also explored how factors like:

⚙️ Thread pitch
🧽 Friction coefficient
🔢 Number of engaged threads

…affect the results. Spoiler: the method is robust even when these change. 👍

📊 Key Findings in Simple Terms

Here’s what they discovered:

• The first thread always carries the most stress and reaches yield first.
• As that thread goes plastic, the load shifts to the next one, and so on.
• Their model predicts how this happens—without needing a slow simulation every time.
• For ISO threads, the plastic load capacity is very close to the ultimate tensile capacity of the screw. That means they’re already well-optimized!
• Changes in friction, thread count, and pitch can be modeled quickly using this method.

🧠 And because the math is efficient, this method can be used in iterative designs and digital twins—where models must run fast and often.

🔮 Future Prospects: What Comes Next?

The authors outline several exciting next steps:

1. More realistic materials: Right now, they use elastic–perfectly plastic models. Adding strain hardening (materials that get stronger as they deform) would improve things further.
2. Non-uniform threads: In real life, threads vary in shape and quality. Modeling this will make results even more accurate.
3. Advanced friction models: Including roughness and load-dependent friction could make the joint behavior more true-to-life.
4. Digital twins for structural health monitoring: The method is fast enough to plug into large-scale simulation platforms for bridges, offshore platforms, or machinery.
5. Load-based design optimization: Engineers can use this tool to find the “sweet spot” for thread designs without wasting time or computing power.

🏁 Wrapping Up: Why This Research Matters

This research hits the sweet spot between accuracy and speed, making it incredibly useful for:

• Civil and mechanical engineers designing bolted joints
• Aerospace and automotive applications where weight and stress matter
• Structural health monitoring (using digital twins)
• Iterative simulations during product design phases

🌍 Imagine reducing bolt failures in wind turbines or improving engine fastener reliability with a few fast calculations. That’s the power of this method.

Concepts to Know

🔩 Threaded Connection - A mechanical joint made by screwing a bolt into a nut—like the ones holding your car wheels or bridge beams together.

⚙️ Elastic Deformation - When a material is stretched or compressed but springs back to its original shape once the load is removed—like a rubber band that hasn’t snapped yet. - Explore this concept further in the "Interactive Stress-Strain Curve Generator ⚙️ 📈📉".

🧱 Plastic Deformation - Permanent change in shape when a material is stressed too much—think of a bent paperclip that doesn’t return to its original form. - Explore this concept further in the "Interactive Stress-Strain Curve Generator ⚙️ 📈📉".

🧮 Analytical Method - A math-based way to solve engineering problems using formulas and logic—no heavy computer simulations needed.

💻 Finite Element Analysis (FEA) - A digital simulation technique that breaks a structure into small pieces (elements) to see how it behaves under loads—super accurate but slow and resource-hungry. - More about this concept in the article "🌈 Vibration-Busting Bars: The Future of Structural Engineering?".

📐 Compliance - A measure of how much something bends or stretches under a force—higher compliance = more flexible.

📏 Stress Concentration - A spot in a material where stress builds up—usually where there's a sharp edge or notch—making it more likely to fail there.

🌡️ Yield Point / Yield Limit - The stress level where a material stops behaving elastically and starts deforming permanently—past this point, there's no going back! - Explore this concept further in the "Interactive Stress-Strain Curve Generator ⚙️ 📈📉".

🧪 Von Mises Stress - A calculated stress value that helps predict when a material will yield—used in engineering to safely design parts. - More about this concept in the article "🔧 Supercharging Seatbelt Safety: AI-Driven Design Slashes Weight by 77%".

🧱 Elastic–Perfectly Plastic Material - A simplified model of a material that stretches elastically up to a point, then deforms plastically without getting any stronger.

🔂 Load Distribution - How force is spread across different parts of a structure—ideally even, but in real life (like threaded joints) it’s usually uneven.

🧊 Digital Twin - A virtual copy of a physical system (like a machine or structure) that helps monitor, predict, and optimize performance in real time. - More about this concept in the article "RoboTwin 🤖🤖 How Digital Twins Are Supercharging Dual-Arm Robots!".

Source: Brutti, C.; Groth, C.; Biancolini, M.E. A Fast Analytical Method for Elastic–Plastic Analysis of Threaded Connections. Appl. Mech. 2025, 6, 42. https://doi.org/10.3390/applmech6020042

From: University of Rome Tor Vergata.